Collision problems of random walks in two-dimensional time

Collision Problems of Random Walks in Two-Dimensional Time*

Let (Xij: i > 0, i > 0} be a double sequence of independently, identically distributed random variables (i.i.d.) which takes values in the d-dimensional integer lattice Ed . The double sequence {Sm,,: m > 0, n > 0} defined by Sllan= xy=, zyW, Xgj is called the random walk in two-dimensional time generated by 41, or a two-parameter random walk, or simply a random walk when there is no danger of ...

Geometrical aspects of quantum walks on random two-dimensional structures

We study the transport properties of continuous-time quantum walks (CTQWs) over finite two-dimensional structures with a given number of randomly placed bonds and with different aspect ratios (ARs). Here, we focus on the transport from, say, the left side to the right side of the structure where absorbing sites are placed. We do so by analyzing the long-time average of the survival probability ...

Time of random walks

Deterministic Random Walks on the Two-Dimensional Grid

Jim Propp’s rotor router model is a deterministic analogue of a random walk on a graph. Instead of distributing chips randomly, each vertex serves its neighbors in a fixed order. We analyze the difference between Propp machine and random walk on the infinite two-dimensional grid. It is known that, apart from a technicality, independent of the starting configuration, at each time, the number of ...

One-dimensional discrete-time quantum walks on random environments

We consider discrete-time nearest-neighbor quantum walks on random environments in one dimension. Using the method based on a path counting, we present both quenched and annealed weak limit theorems for the quantum walk.